To create a model of the subsurface is to construct a discretized representation (volumetric grid) of a complex 3D domain which is adapted to the domain's material properties such as permeability. In general, the domain is comprised of multiple separate volumetric pieces which may come in partial contact with each other, thus, forming a non-manifold topology. The domain's material properties are described by a designer who can assign them to only one continuous volume at a time. Material properties are described as piecewise smooth implicit or explicit functions (e.g., piecewise constant) in 3D.
For example, in application to subsurface reservoir modeling, a 3D model domain is delineated by horizons and faults, where horizons are mostly flat horizontal surfaces related to deposition of sediment material forming a reservoir rock, and faults are discontinuities in the rock introduced by non-depositional events. For a modeler to provide a description of rock properties in the subsurface domain, it is necessary to work in a continuous “depositional” space (i.e., a design space) where all the faults have been removed. Rock properties then can be described with the help of globally continuous trend functions and/or mesh dependent functional representations in this continuous space. A volumetric grid in physical space that conforms to the rock properties is required to carry out modeling and flow simulation studies. For purposes of this application, a grid is the conceptual subdivision of a subsurface region into adjacent discrete cells for the purpose of specifying a numerical value for one or more material properties of the subsurface such as rock type, permeability or porosity for each cell.
Related publications dealing with the same or similar technical problem include “Unstructured Cut-Cell Grids for Modeling Complex Reservoirs,” B. T. Mallison, C. Sword, T. Viard, W. J. Milliken, A. Cheng, SPE163642 (2013). The authors use GeoChron mapping, build a structured grid in a design space, and truncate it by images of fault surfaces, then map truncated cells back to real space and do complex post-processing on the fault surfaces. This approach is time consuming, and requires well-defined inverse mapping (back to real space) and complex geometric post-processing.
In US patent application publication US 2008/0021684 (“Method for building a three dimensional cellular partition of a geological domain,” by J.-C. Dulac, J.-L. Mallet), the authors define “parametric” mapping to design space (GeoChron), voxelize real space and sample cell ID or layer ID from the design space (partitioned into “parametric” cells, i.e. a Cartesian grid). They do not define cell geometry or topology in real space but instead do post-processing on the aggregations of voxels with the same cell ID to use them as cells in a flow simulator. This avoids the complexity of building the 3D simulation mesh in real space, requires voxelization (which requires accuracy of the mapping and/or inverse mapping) and post-processing of voxels into simulation cells by deducing or approximating their geometric and topological relationships, none of which is straightforward.
U.S. Pat. No. 7,523,024 to Endres et al., “Modeling geologic objects in faulted formations,” defines geological objects in real space (construct a geobody in design space, map it back to real space using inverse “paleo-transformation,” and trim the portions that map outside). Their approach requires inverse mapping, and does not go all the way to grid generation.
Patent application publication No. WO2012/078217 to Wu et al. discloses mapping the physical domain to a continuous design space.
In summary, the main approach in the current advanced subsurface grid generation strategies is to define a two-way mapping to design space, build a volumetric grid in the design space, and populate it with properties, then map the grid geometry back to real space (as stair-step by Dulac et al. or as truncated by Mallison et al.). A more traditional approach is to define a grid in real space with standard layering methods (proportional, top- or bottom-conforming) without much regard for the property trends/shape of the geobodies, then map the grid to design space and populate it with properties.